To a non-Christian soldier in AIT, getting the extra privileges and having some fun are worth the price of having to sit through the fundamentalist Christian sermons that go along with these activities, so many of them do it. Others go along simply because they don't want to stand out from the crowd and be singled out as being of the "wrong" religion or not being religious.
Cadence particularly targets soldiers in AIT for a reason -- these are the soldiers likely to soon be facing their first deployment. And this ministry, which, as noted above receives DoD contracts for their work, makes no secret of why they've chosen AIT as its mission field. One of the reasons given by Cadence for the success of its "Strategic Ministry" is: "Deployment and possibly deadly combat are ever-present possibilities. They are shaken. Shaken people are usually more ready to hear about God than those who are at ease, making them more responsive to the gospel." Of course, they must first gain access to these "shaken" soldiers, but that's no problem -- the Army helps them out by allowing them to operate on Army posts and granting the soldiers in AIT extra privileges if they attend Cadence's retreats.
For more details on these and other taxpayer funded schemes to Christianize the U.S. military, see "Against All Enemies, Foreign and Domestic," the chapter I wrote for the 2010 book Attitudes Aren't Free: Thinking Deeply about Diversity in the US Armed Forces, published by Air University Press, the publishing arm of the Air Force's Air University at Maxwell Air Force Base.